I don't think that Klopp will suffer the same fate as Tuchel, but even if it happens it is of course a loss for Liverpool because it is difficult to find a coach as good as Klopp at the moment, Liverpool deteriorating performance does not seem to be due to Klopp strategy error but none other than because of his performance their players are indeed deteriorating, losing Mane, I think is one of the reasons for Liverpool current bad performance and Nunez has not been able to have an effect on Liverpool game, yesterday defeat against Napoli was quite painful but if we look at Liverpool defenders they performed quite badly in the match.
Yes, Klopp is still safe at Liverpool because he is a coach who has the respect of the fans of his team and club. Klopp needs a lot of support to improve Liverpool's current form and morale, but that will soon be different when they start the competition again next week. Chelsea were impatient with Tuchel, they did not learn from Arsenal who kept Arteta despite Arsneal's poor performance.
Now Klopp's task is certainly difficult considering Liverpool do not have good players to navigate this tight competition. They lost a few players through injury, and that has cost them some strength against big teams like Manchester United and Napoli.